1. Field of the Invention
This invention is related to methods for acquiring and processing nuclear magnetic resonance (NMR) measurements for determination of longitudinal and transverse relaxation times T1 and T2. Specifically, the invention deals with methods for acquiring NMR measurements using a modified CPMG sequences with a variable interecho spacing.
2. Description of the Related Art
Nuclear magnetic resonance is used in the oil industry, among others, and particularly in certain oil well logging tools. NMR instruments may be used for determining, among other things, the fractional volume of pore space and the fractional volume of mobile fluid filling the pore space of earth formations. Methods of using NMR measurements for determining the fractional volume of pore space and the fractional volume of mobile fluids are described, for example, in xe2x80x9cSpin Echo Magnetic Resonance Logging: Porosity and Free Fluid Index Determination,xe2x80x9d M. N. Miller et al., Society of Petroleum Engineers paper no. 20561, Richardson, Tex., 1990. Further description is provided in U.S. Pat. No. 5,585,720, of Edwards, issued Dec. 17, 1996 and having the same assignee as the present application, entitled xe2x80x9cSignal Processing Method For Multiexponentially Decaying Signals And Applications To Nuclear Magnetic Resonance Well Logging Tools.xe2x80x9d The disclosure of the Edwards patent is fully incorporated herein by reference.
Deriving accurate transverse relaxation time T2 relaxation spectra from nuclear magnetic resonance (NMR) data from logging subterranean formations, or from Cores from such formations, is critical to determining total and effective porosities, irreducible water saturations, and permeabilities of the formations. As discussed in Prammer (U.S. Pat. No. 6,005,389), the total porosity is the fractional volume of a rock that is occupied by fluids. The total porosity (e.g. measured by a density tool) includes clay bound water that typically has extremely short relaxation times, moveable water and hydrocarbons that have long relaxation times, and capillary bound water that has intermediate relaxation times. The effective porosity is defined as that portion of the pore volume containing fluids that are moveable, i.e., the total porosity minus the clay bound water. Accurate spectra are also essential to estimate T2 cutoff values and to obtain coefficients for the film model or Spectral Bulk Volume Irreducible (SBVI) model. Effective porosities are typically summations of partial porosities; however, distortion of partial porosity distributions has been commonly observed for a variety of reasons. These reasons include poor signal-to-noise ratio (SNR), and poor resolution in the time domain of the NMR data.
U.S. Pat. No. 6,069,477 to Chen et al having the same assignee as the present application discusses the constituents of a fluid saturated rock and various porosities of interest. Referring to FIG. 1, the solid portion of the rock is made up of two components, the rock matrix and dry clay. The total porosity as measured by a density logging tool is the difference between the total volume and the solid portion. The total porosity includes clay-bound water, capillary bound water, movable water and hydrocarbons. The effective porosity, a quantity of interest to production engineers is the sum of the last three components and does not include the clay bound water.
The most common NMR log acquisition and core measurement method employs T2 measurements using CPMG (Carr, Purcell, Meiboom, and Gill) sequence, as taught by Meiboom and Gill in xe2x80x9cModified Spin-Echo Method for Measuring Nuclear Relaxation Time,xe2x80x9d Rev. Sci. Instrum. 1958, 29, pp. 688-691. In this method, the echo data in any given echo train are collected at a fixed time interval, the interecho time (TE). Usually, a few hundred to a few thousand echos are acquired to sample relaxation decay. However, for determination of CBW, echo sequences of as few as ten echos have been used.
Interecho time (TE), is one of the most important, controllable experimental parameters for CPMG measurements and can affect data interpretation. In logging operations using the MRIL(copyright) tool (made by Numar Corp.), TEs of 0.6 and 1.2 milliseconds (ms) are typically used to manipulate the relaxation decay data to include or exclude clay bound water (CBW) porosity.
Interpretation of NMR core or log data is often started by inverting the time-domain CPMG echo decay into a T2 parameter domain distribution. In general, the T2 of fluids in porous rocks depends on the pore-size distribution and the type and number of fluids saturating the pore system. Because of the heterogeneous nature of porous media, T2 decays exhibit a multiexponential behavior. The basic equation describing the transverse relaxation of magnetization in fluid saturated porous media is                               M          ⁡                      (            t            )                          =                              ∫                          T                              2                ⁢                min                                                    T                              2                ⁢                max                                              ⁢                                    P              ⁡                              (                                  T                  2                                )                                      ⁢                          ⅇ                                                -                  t                                /                                  T                  2                                                      ⁢                          ⅆ                              T                2                                                                        (        1        )            
where M is magnetization, and effects of diffusion in the presence of a magnetic field gradient have not been taken into consideration. Eq.(1) is based on the assumption that diffusion effects may be ignored. In a gradient magnetic field, diffusion causes atoms to move from their original positions to new ones which also causes these atoms to acquire different phase shifts compared to atoms that did not move. This contributes to a faster rate of relaxation.
The effect of field gradients is given by an equation of the form                               1                      T            2                          =                              1                          T                              2                ⁢                bulk                                              +                      1                          T                              2                ⁢                surface                                              +                      1                          T                              2                ⁢                diffusion                                                                        (        2        )            
where the first two terms on the right hand side are related to bulk relaxation and surface relaxation while the third term is related to the field gradient G by an equation of the form                               T                      2            ⁢            diffusion                          =                  C                      T            ⁢                          xe2x80x83                        ⁢                                          E                2                            ·                              G                2                            ·              D                                                          (        3        )            
where TE is the interecho spacing, C is a constant and D is the diffusivity of the fluid.
In CPMG measurements, the magnetization decay is recorded (sampled) at a fixed period, TE; thus, a finite number of echos are obtained at equally spaced time intervals, t=n TE, where n is the index for the n-th echo. This may be denoted by                               M          ⁡                      (                          n              ⁢                              xe2x80x83                            ⁢              T              ⁢                              xe2x80x83                            ⁢              E                        )                          =                                            ∫                              T                                  2                  ⁢                  min                                                            T                                  2                  ⁢                  max                                                      ⁢                                          P                ⁡                                  (                                      T                    2                                    )                                            ⁢                              ⅇ                                                                            -                      n                                        ·                    T                                    ⁢                                      xe2x80x83                                    ⁢                                      E                    /                                          T                      2                                                                                  ⁢                              ⅆ                                  T                  2                                                              +                      n            ⁢                          xe2x80x83                        ⁢            o            ⁢                          xe2x80x83                        ⁢            i            ⁢                          xe2x80x83                        ⁢            s            ⁢                          xe2x80x83                        ⁢            e                                              (        4        )            
A problem associated with conventional CPMG sequences is that the resolvability of the T2 spectrum is not uniform. Short T2 s are poorly resolved as only a few data points are affected by these components. Long T2 s, on the other hand, are oversampled. In addition, due to limitations on availability of power, the number of pulses is limited: this has the undesirable effect of leading to poor resolution of short T2 components because measurements have to be made over long time to resolve the slowly relaxing components. The actual selection of TE and number of pulses involves a tradeoff governed by the power availability and the desire for rapid acquisition to keep down rig costs.
As discussed in U.S. Pat. No. 6,069,477 to Chen et al, the contents of which are fully incorporated herein by reference, the effects of noise, sampling rate, and the ill-conditioning of inversion and regularization are to smear (broaden) the estimated T2 distribution. In addition, because of the non-orthogonality of multi-exponential signals, CBW signals could be shifted to higher T2 regions if the T2 fitting region is limited or if the regularization is excessive. This distortion is not easily rectified; even adding more bins with short T2 does not reduce the distortion of the T2 spectra.
Chen et al teaches the use of CPMG sequences with two different values of TE (0.6 ms and 1.2 ms). A time domain correction is used to filter out the contribution of the fast relaxing T2 components in the TE=1.2 ms echo train. High S/N echo data with sampling time TE=0.6 ms are used to obtain the CBW T2 distribution. These data are then used to reconstruct CBW contributions to the time domain early echos of the conventional effective porosity echo data (TE=1.2 ms). The CBW signal is then subtracted from the original echos, and the effective porosity distribution is estimated from the reconstructed echo train. Other methods can be applied to jointly process echo train data with different TEs (e.g., Dunn et al., 1998, xe2x80x9cA method for inverting NMR data sets with different signal to noise ratiosxe2x80x9d paper JJ, in 39th annual logging symposium transactions SPWLA).
The use of two different CPMG sequences with different values of TE may still lead to erroneous results in measurement-while-drilling applications. The reason is that due to tool motion, the sensitive volume may be different for the first and second CPMG sequence. The region of investigation for an NMR logging tool is defined by the region in the formation wherein the Larmor frequency of nuclear spins matches the RF frequency of the tipping pulse. Subsequent refocusing pulses in a CPMG sequence will produce spin-echo signals from this region. When the tool is in motion, as in a MWD logging tool, the region of investigation may be different for successive CPMG sequences, so that the spin echos for a second CPMG sequence may not come from the same region as the spin echos for a first CPMG sequence. It would be desirable to have a method of obtaining an NMR spectrum of a medium with a resolution that is more uniform over the range of spectral values and that is not sensitive to tool motion, particularly in MWD applications. Such a method should preferably also have reduced power consumption. The present invention satisfies this need.
The present invention is a method of acquiring NMR spin echo signals using pulse sequences having more than one interecho spacing. This makes it possible to acquire relaxation spectra with high resolution of rapidly relaxing components and reduced power requirements over the slowly relaxing portions of relaxation spectra. Multiple TE data may be acquired when different types of fluids are present in the formation to resolve the fast decaying components as well as the slow decaying components. In a gradient field the diffusion effect has to be considered for selection of proper TE values.
In a preferred embodiment, the method is used with a zero gradient magnetic field configuration. This reduces the effects of diffusion on the echo signals. Power requirements may be further reduced by using refocusing pulses with an angle of less than 180xc2x0.
Signal to noise ratio may be further improved by using a plurality of pulse sequences and stacking the resulting signals. By proper selection of the variable TE sequences a desired resolution may be obtained for all expected components (short, medium, and long) while reducing the required time and the required power. This is particularly important in the resolution of short T2 components.
When used for measurement-while-drilling, optional embodiments of the invention use motion sensors on the drilling assembly and the timing of the pulses in the pulse sequences is based in part on the output of the motion sensors. Optionally, predictive filtering of the motion signals may be used to further improve the signal to noise ratio.